President Obama, followed by Elizabeth Warren, head the Consumer Financial Protection Bureau, walks to the Rose Garden of the White House in Washington, on Monday, July 18.

Pablo Martinez Monsivais/AP/File

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Washington — Harvard law professor Elizabeth Warren filed paperwork Thursday to form an exploratory committee for a Senate run, setting up a potentially competitive race with Republican Sen. Scott Brown of Massachusetts.

The Massachusetts race is one of the few in 2012 where a Democrat has a shot at capturing a Republican-held seat. Though Senator Brown is reasonably popular, he represents a deeply blue state, and handicappers call a Brown-Warren race a tossup.

Brown won the seat in a special-election upset in January 2010, following the death of Sen. Edward Kennedy (D). Tea party money came in from all over the country, adding momentum to the low-tax, small-government movement when Brown won.

Ms. Warren is best known for advocating creation of the Consumer Financial Protection Bureau (CFPB), a body mandated by the financial reform legislation of 2010. The outspoken liberal became a lightning rod on the issue, making her a favorite of progressives and a boogeyman for conservatives.

President Obama did not nominate her to be the first head of the agency, knowing Senate confirmation would have been nearly impossible. Instead, he made her a special adviser to the Treasury secretary for the CFPB. She left the administration on Aug. 1 and returned to Harvard.

“She definitely brings a different résumé to the race,” Ms. Duffy says. “It’s going to have its pluses and minuses. The big thing is that she’ll be a magnet for national money. Of course, that’s going to help Brown raise money.”

Brown is one of the more moderate Republicans running for reelection in this cycle, but so far he faces no serious tea party challenge for the GOP nomination. Warren, a native of Oklahoma, could square off against a half-dozen Democratic candidates, though the only one with any money is Alan Khazei, former CEO of the City Year youth service program.

Warren has never run for office before, and it’s unknown how she will perform on the stump.

“Beyond her identification as a Democrat, I think her biggest asset is that she’s aggressive, which will play well after [Martha] Coakley,” says Jeffrey Berry, a political scientist at Tufts University outside Boston.

State Attorney General Coakley was the Democratic nominee in 2010 against Brown, and she ran a lackluster campaign in an election that was widely seen as hers to lose.

“Warren’s weak spot is that she’s an academic, and it’s not clear that she can relate to the average voter,” Mr. Berry says. “Brown has great facility in exuding a common touch and a regular home-boy persona.”

Still, he calls a Warren-Brown race a tossup, given registered Democrats’ strong numerical advantage in Massachusetts over Republicans.

Control of the Senate hangs in the balance in 2012, with the Democrats currently holding 53 of the 100 seats. Of the 33 seats up for election, 23 are held by Democrats and 10 by Republicans. Of those, seven Democratic-held seats and two Republican-held seats are listed as tossups on the Cook Political Report scorecard.

Warren is starting her exploratory phase with a “listening tour.” First out of the block with cheers was EMILY’s List, which supports Democratic women candidates who favor abortion rights.

“I’m thrilled that Elizabeth is pursuing this next endeavor with the thoughtfulness and respect that’s been such a hallmark of her career,” said Stephanie Schriock, president of EMILY’s List, in a statement. “Starting a listening tour is not only a great way to find out what folks need, it’s a perfect contrast to Republican Scott Brown, who has yet to hold a single public town hall.”

“As a native of Oklahoma, the anointed candidate of the Washington establishment, and someone who has spent many years ensconced in the hallways of Harvard, it’s a good idea for Professor Warren to learn more about her adopted state of Massachusetts as she prepares to compete in a crowded Democrat primary,” said Brian Walsh, communications director of the NRSC, in a statement. “If she’s really listening, she’ll hear that her plans for higher taxes and more Washington spending will kill jobs.”